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QCE Stuff => QCE Mathematics Subjects => QCE Subjects + Help => QCE Specialist Mathematics => Topic started by: Pablo1204 on October 06, 2021, 09:35:24 pm

Title: Vector Calc Question
Post by: Pablo1204 on October 06, 2021, 09:35:24 pm: Hello,

Could someone please help me find where I went wrong in this projectile motion question.

Question:
A ball is thrown at ground level from origin O with initial speed of 50m/s. There is a wall 100 m to the right of O which is 20 m tall. Find the smallest possible projection angle such that the ball passes over the building. Use g=9.8

I got that the position vector is $r(t)=(50tcos(\theta))i + (50tsin(\theta)-\frac{1}{2}gt^2)j$

Then subbed in $r(t)=(100)i+(20)j$

Which resulted in the projection angle being equal to 23.40 degrees however the textbook got 23.33 degrees.

Thanks
Title: Re: Vector Calc Question
Post by: RuiAce on October 06, 2021, 09:45:22 pm: I played around with technology for this. WolframAlpha seems to suggest that $\theta \approx 23.398^\circ$, so your answer should be correct (with rounding). I then checked on Desmos, and with $\theta \approx 23.33^\circ$ I found that the ball doesn't clear the wall either.

The working you had provided seemed correct to me.
Title: Re: Vector Calc Question
Post by: Pablo1204 on October 06, 2021, 09:49:34 pm: Alright thank you for the clarification